Beyond Rise Over Run: A Learning Trajectory for Slope

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Frederick A. PeckUniversity of Montana

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This article presents the results of a design-based research study related to slope that took place in a high school algebra 1 classroom. In the study, students explored situations related to making predictions. As students engaged with these situations, they reinvented and made meaningful multiple subconstructs of slope. I present the findings in the form of a learning trajectory for slope, which describes how learning happened over time, the principles that guide the design of activities that support this learning, and the rationale for how the activities support learning.

Footnotes

Most of all, thank you to the students who participated in this study. I learned a lot from you. I am grateful for the invaluable contributions of Raymond Johnson, Michael Matassa, David Webb, and the other members of the research team. I am especially indebted to Michael, who shared many late nights and early mornings with me throughout this study. This article is based on my dissertation, and I deeply thank my committee—David Webb, Kris Gutiérrez, Victoria Hand, William Penuel, and Luis Radford—for their support and mentorship. Special thanks to my chair, David Webb, who literally made this study possible when he brought the Freudenthal Institute US to the University of Colorado and encouraged me to participate in its research. Thanks to Carrie Allen, Margaret Eisenhart, Sara Heredia, Eve Manz, Joanna Weidler-Lewis, and the anonymous reviewers for their helpful comments and suggestions that greatly improved this article.

Contributor Notes

Frederick A. Peck, Department of Mathematical Sciences, University of Montana, 32 Campus Drive #0864, Missoula, MT 59812; frederick.peck@umontana.edu

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